Reference calibration for an adaptive optics system

ABSTRACT

A method of determining a reference calibration setting for an adaptive optics system comprising a detecting device for detecting light from an object; and at least one controllable wavefront modifying device arranged such that light from the object passes via the wavefront modifying device to the detecting device. The method comprises: arranging a light-source between the object and the wavefront modifying device to provide a reference light beam to the detecting device; for each of a plurality of orthogonal wavefront modes: controlling the wavefront modifying device to vary a magnitude of the orthogonal wavefront mode; acquiring a series of readings of the detecting device, each reading corresponding to one of the magnitude; determining a quality metric value for each reading, resulting in a series of quality metric values; and determining a reference parameter set for the wavefront modifying device corresponding to an optimum quality metric value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a 371 U.S. National Stage of InternationalApplication No. PCT/EP2012/069620, filed Oct. 4, 2012, which claimspriority to EP Application No. 11184413.0, filed Oct. 7, 2011. Thedisclosure of each of the above applications is incorporated herein byreference in their entirety.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a method of determining a referencecalibration setting for an adaptive optics system comprising a detectingdevice for detecting light from an object, and at least one controllablewavefront modifying device arranged such that light from said objectpasses via said wavefront modifying device to said detecting device. Thepresent invention also relates to such an adaptive optics system.

TECHNICAL BACKGROUND

Adaptive optics has been applied in different areas of science andindustry, e.g. to enhance the capabilities of imaging systems inastronomy, microscopy, and ophthalmology, to enhance signal quality inoptical communication systems, and also in laser beam control. Inenvironments where an imaging system is used to observe objects behind acontinuously evolving phase curtain (atmosphere, ocular optics, heatingeffects, etc.), the adaptive optics system can effectively mitigate theeffects of this medium to regain the loss of imaging performance.

The purpose of an adaptive optics system is to correct aberrations, orphase errors, thereby reducing the phase variance. However, in manyadaptive optics systems, the wavefront sensor is relative (e.g. aShack-Hartmann sensor), meaning that static errors are unseen if notcalibrated correctly. Even with an absolute wavefront sensor, non-commonpath errors specific to the detecting path imply an aberratedimaging/detecting channel. It is therefore crucial to reduce theseeffects to achieve optimal performance of the adaptive optics system.

One way of achieving a reference calibration for a wavefront sensorwould be to provide a reference plane wave and to register the output ofthe wavefront sensor in response to that reference plane wave. It,however, appears difficult and costly to achieve such a perfect planewave.

U.S. Pat. No. 6,609,794 discloses an alternative method for referencecalibration of an adaptive optics system using a modified Shack-Hartmannsensor as a wavefront sensor. According to U.S. Pat. No. 6,609,794, eachlenslet in the lenslet array comprised in the Shack-Hartmann sensor isprovided with a substantially opaque element in the center of thelenslet. By illuminating the thus modified Shack-Hartmann sensor with areference beam, a reference or zero-point reading can be acquired.

Although the approach of U.S. Pat. No. 6,609,794 seems to represent asimplified way of achieving a reference calibration of a wavefrontsensor, there is still room for improvement. For example, a special kindof wavefront sensor is required and aberrations in the detecting pathare not taken into account.

SUMMARY OF THE INVENTION

In view of the above-mentioned and other drawbacks of the prior art, ageneral object of the present invention is to provide for an improvedreference calibration of an adaptive optics system.

According to a first aspect of the present invention, these and otherobjects are achieved through a method of determining a referencecalibration setting for an adaptive optics system comprising: adetecting device for detecting light from an object; and at least onecontrollable wavefront modifying device arranged such that light fromthe object passes via the wavefront modifying device to the detectingdevice, the method comprising the steps of: arranging a light-sourcebetween the object and the wavefront modifying device to provide areference light beam to the detecting device via the wavefront modifyingdevice; for each of a plurality of orthogonal wavefront modes of thewavefront modifying device: controlling the wavefront modifying deviceto vary a magnitude of the orthogonal wavefront mode over apredetermined number of magnitude settings; acquiring a series ofreadings of the detecting device, each reading corresponding to one ofthe magnitude settings; determining a quality metric value indicative ofan information content of the reading for each reading in the series ofreadings, resulting in a series of quality metric values; anddetermining a reference parameter set for the wavefront modifying devicecorresponding to an optimum quality metric value based on the series ofquality metric values.

An “adaptive optics system” is an optical system with adaptivecapability for compensating for static and/or non-static opticalaberrations introduced by the medium between an object and a detectingdevice. Adaptive optics systems are used for improved detection in suchdiverse fields as ophtalmology, astronomy, microscopy, and opticalcommunication. The “object”, obviously, may be different depending onfield of application. In the case of ophtalmology, the “object” may, forexample, be the retina. In astronomy applications, the “object” may, forexample, be a star or a nebula. In optical communication, the “object”may, for example, be a transmitter telescope. In order to provide forthe adaptive compensation of non-static optical aberrations, adaptiveoptics systems include a wavefront sensor for providing informationabout the (time-varying) spatial phase distribution of the lightincident on the wavefront sensor and a wavefront modifying device formodifying the spatial phase distribution of the light based on signalsfrom the wavefront sensor. After having been modified by the wavefrontmodifying device, the light from the object is directed towards adetecting device.

In the context of the present application, the term “wavefront modifyingdevice” should be understood to mean any device that is controllable tomodify the wavefront (spatial phase distribution) of light incident onthe wavefront modifying device. Examples of such wavefront modifyingdevices include, for example, deformable mirrors, optically addressedspatial light modulators, electrically addressed spatial lightmodulators, etc.

The “detecting device” may be any device capable of detecting one orseveral properties of the light from the object. Such properties may,for example, include maximum intensity, intensity distribution,wavelength distribution, phase distribution etc. Examples of suitabledetecting devices include a photodiode and an imaging device, such as acamera.

The spatial phase distribution (the shape of the wavefront) may beexpressed in terms of a sum of “wavefront modes” with differentcoefficients/weights. In analogy, the wavefront modification of awavefront modifying device (such as the shape of a deformable mirror)may also be expressed in terms of a sum of wavefront modes. Examples oforthogonal wavefront modes include so-called Zernike modes, butwavefronts/wavefront modifications may be expressed using several otherkinds of orthogonal wavefront modes such as, for example, Legendrepolynomials or Karhunen-Loève polynomials.

Furthermore, the “information content” of a reading of the detectingdevice is a property that indicates how close to aberration-free theacquired reading is. This property will depend on the reference beamused and the type of detecting device. For example, an acquired imagethat closely resembles a reference image has a higher informationcontent than an acquired image that differs significantly from thereference image. In simpler embodiments a high acquired intensity may bedetermined to have a higher information content than a lower acquiredintensity. Similarly, the higher the contrast of an image or detectorreading, the higher the information content is. In optical communicationapplications, the information content can be said to be represented bythe signal-to-noise ratio.

The present invention is based on the realization that an improvedreference calibration can conveniently be achieved by performing a“partial calibration” for each of a plurality of orthogonal wavefrontmodes of the wavefront modifying device and, for each of these “partialcalibrations”, optimizing the information content obtained at thedetecting device.

Since the method according to the present invention uses readings at thedetecting device, rather than at the wavefront detector, aberrationsalong the detecting path are also calibrated for. This provides for animproved reference calibration.

According to various embodiments of the present invention the adaptiveoptics system may be configured such that it includes: a common pathbetween the object and a beam splitting device, the common pathincluding the at least one controllable wavefront modifying device; adetecting path between the beam splitting device and the detectingdevice; and a sensing path between the beam splitting device and thewavefront sensor. Signals from the wavefront sensor may be used tocontrol the wavefront modifying device.

In embodiments including a beam splitting device, the “beam splittingdevice” may be any device capable of connecting the common path to thedetecting path and to the sensing path. The routing provided by the beamsplitting device may be static or dynamic. Static routing may, forexample, be provided by a beam splitting device, such as a beamsplitter. Dynamic routing may be achieved by a controllable beamdeflection device, such as a mirror or other suitable optical element,or an optical switch. In the case of dynamic routing, a light beamincident on the beam splitting device from the common path may becontrolled to alternatingly follow the detecting path and the sensingpath.

According to various embodiments of the present invention, theorthogonal wavefront modes may be determined based on an interactionmatrix defining a relation between different wavefront modifying statesof the controllable wavefront modifying device and corresponding signalsfrom the wavefront sensor.

Hereby, the result of the relative calibration (the relation betweendifferent settings of the wavefront modifying device and correspondingresponse signals from the wavefront sensor) can be re-used for thereference calibration, which facilitates the reference calibration.

Moreover, the orthogonal wavefront modes may be determined usingsingular value decomposition of the interaction matrix, which furtherfacilitates the reference calibration, since it is a straightforwardmodal decomposition of the adaptive optics system without furtherapproximation.

Furthermore, the method according to the above embodiments of theinvention may further comprise the steps of controlling the wavefrontmodifying device to a plurality of different wavefront modifying states;registering, for each of the wavefront modifying states, a correspondingsignal from the wavefront sensor; and determining the interaction matrixbased on the plurality of different wavefront modifying states and thecorresponding signals from the wavefront sensor.

According to the present invention, a reference parameter set isdetermined for each wavefront mode. By applying the reference parameterset of a particular mode before optimizing the quality metric value forthe next wavefront mode, it has been empirically established that feweriterations are generally required to arrive at a satisfactory referencesetting for the adaptive optics system. Alternatively, the referenceparameter set for each wavefront mode may be stored in memory and thereference setting may be determined based on the reference parametersets stored in the memory. In this case, the reference setting may bedetermined to be a suitable combination of the reference parameter sets.

According to various embodiments of the method according to the presentinvention, the step of determining the reference parameter set maycomprise the step of fitting the series of quality metric values to apredetermined function having a maximum or minimum corresponding to aminimum aberration of the wavefront mode.

This predetermined function may vary depending on the type of referencebeam used. For a reference beam originating from a point source, forexample, the predetermined function may be a Gaussian function or aquadratic function.

Although the method according to various embodiments of the presentinvention is applicable for readings from various detecting devicescapable of detecting intensity variations in the light impinging on thedetecting device, the detecting device may advantageously be an imagingdevice and the readings of the detecting device may be images.

In embodiments where the detecting device is an imaging device, such asa CCD-sensor or a CMOS-sensor, the step of determining quality metricvalues may comprise the step of transforming each image in the series ofimages from a spatial domain to a Fourier domain, which will maximizethe information content and improve the precision in the determinationof the quality metric values.

In the case when the imaging device comprises an image sensor having aplurality of pixels, the step of determining quality metric values mayadvantageously further comprise the step of summing a product of theFourier transform of the image intensity and a measure indicative of adistance from the position of maximum intensity for each pixel in of theimage sensor.

As mentioned above, the source of the reference beam may be a pointsource. In such embodiments, each of the quality metric values mayadvantageously be indicative of a Strehl ratio of an associated readingof the detecting device.

According to a second aspect of the present invention, theabove-mentioned and other objects are achieved through an adaptiveoptics system for providing aberration compensated detection of lightfrom an object, the adaptive optics system comprising: a detectingdevice for detecting light from an object; a wavefront sensor configuredto provide signals indicative of a spatial phase distribution of lightincident on the wavefront sensor; at least one controllable wavefrontmodifying device arranged such that light from said object passes viasaid wavefront modifying device to said detecting device and to saidwavefront sensor; a control system connected to the wavefront sensor andto the wavefront modifying device, said control system being operable ina calibration mode and in a regulation mode, wherein said control systemcomprises: an output for providing control signals to the wavefrontmodifying device; a first input for receiving signals from the wavefrontsensor; a second input for receiving readings the detecting device; awavefront modifying device controller for controlling the wavefrontmodifying device; calibration circuitry for determining calibrationparameters for the adaptive optics system; and a memory for storing saidcalibration parameters, wherein: when the control system operates in thecalibration mode: the wavefront modifying device controller, for each ofa plurality of orthogonal wavefront modes of the wavefront modifyingdevice, controls the wavefront modifying device to vary a magnitude ofthe orthogonal wavefront mode over a predetermined number of magnitudesettings; and the calibration circuitry, for each of the plurality oforthogonal wavefront modes, determines a quality metric value indicativeof an information content of each reading in a series of readingsreceived from the detecting device, each reading corresponding to one ofthe magnitude settings, resulting in a series of quality metric values;determines a reference parameter set for the wavefront modifying devicecorresponding to an optimum quality metric value based on the series ofquality metric values for each of the plurality of orthogonal wavefrontmodes; and when the control system operates in the regulation mode: thewavefront modifying device controller regulates the wavefront modifyingdevice based on signals from the wavefront sensors and the referenceparameter set.

The various parts of the control system comprised in the adaptive opticssystem may be embodied as separate components and/or as software in oneor several microprocessor(s).

Further embodiments and effects of this second aspect of the presentinvention are largely analogous to those described above with referenceto the first aspect of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of the present invention will now be describedin more detail, with reference to the appended drawings showing at leastone example embodiment of the invention, wherein:

FIG. 1a schematically shows an adaptive optics system according to anexemplary embodiment of the present invention;

FIG. 1b is a schematic block diagram of the control system comprised inthe adaptive optics system in FIG. 1a ; and

FIG. 2 is a schematic flow chart of a method according to an embodimentof the present invention.

DETAILED DESCRIPTION OF AN EXAMPLE EMBODIMENT OF THE INVENTION

In the below detailed description, example embodiments of the presentinvention are mainly described with reference to an adaptive opticssystem where a point source is used to generate the reference beam andthe detecting device is provided in the form of an image sensor which isused to acquire pixelated images of the point source. Furthermore,so-called guide stars are described as being generated by the adaptiveoptics system.

This should by no means be construed as limiting the scope of thepresent invention, which also encompasses cases when other types ofreference beams are used, which result in another spatial intensitydistribution at the plane of the detecting device. For example, suchreference beams may provide an edge or a checkered pattern at thedetecting device. Furthermore, the detecting device need not be animaging device, but may be a non-imaging detector, such as a photo diodeor equivalent. Moreover, one or several externally provided guide starsmay be used. In astronomy-related applications, for example, one orseveral stars may be used as guide stars.

FIG. 1a schematically shows an exemplary adaptive optics system 1according to an embodiment of the present invention. The adaptive opticssystem 1 in FIG. 1a comprises a common path 2, a sensing path 3, and adetecting path 4. In FIG. 1a , the common path 2 is indicated by adashed line, the sensing path 3 is indicated by a dotted line, and thedetecting path 4 is indicated by a dashed-dotted line. The common path 2is the optical path between the object 5 and a beam splitting device 6,here in the form of a cold mirror, the sensing path 3 is the opticalpath between the beam splitting device 6 and a wavefront sensor 7, andthe detecting path 4 is the optical path between the beam splittingdevice 6 and a detecting device 8. The adaptive optics system 1 in FIG.1a further comprises a controllable wavefront modifying device 9arranged in the common path, and a control system 10 that is connectedto the wavefront modifying device 9, to the wavefront sensor 7, and tothe detecting device 8. In addition, the adaptive optics system 1 inFIG. 1a comprises a guide star light-source 11 and a second beamsplitting device 12, here in the form of a wedge beam splitter. The beamsplitting device 12 redirects one light beam to follow the common path 2to the object 5, where the light-beam provides a so-called guide star,or multiple light beams to follow the common path 2 to the object 5,where the light beams provide multiple guide stars.

When in operation, the adaptive optics system 1 in FIG. 1a corrects fortime-varying aberrations between the object 5 and the wavefront sensor 7by regulating the wavefront modifying device 9 based on the knownposition(s) of the guide star(s). For this correction to work, thereneeds to be a known relation between different states of the wavefrontmodifying device 9 and corresponding readings of the wavefront sensor 7.To achieve this relation, the adaptive optics system 1 needs to becalibrated.

Calibration is accomplished by imaging one point source or multiplepoint sources, via the wavefront modifying device 9, on the wavefrontsensor 7. The position of the point source(s) will vary depending on theapplication field of the adaptive optics system 1 (retinal imaging,astronomy, etc). According to an embodiment of the present invention,one exemplary position for the point source(s) (which may be areflection of the point source(s) formed by the guide star light-source11) is at a suitable position on the common path 2 between the object 5and the controllable wavefront-modifying device 9, designated by “X” inFIG. 1 a.

With the point source(s) in place at the position denoted by “X”, thewavefront modifying device 9 is controlled by the controller betweendifferent wavefront modifying states, and corresponding signals from thewavefront sensor 7 are registered. Based on the different wavefrontmodifying states and the corresponding signals from the wavefront sensor7, a so-called interaction matrix is determined that can be used tocorrelate between changes at the wavefront modifying device 9 andcorresponding changes in the signal from the wavefront sensor 7.

The above-described calibration is a relative calibration in the meaningthat differences between states of the wavefront modifying device 9 arecorrelated to differences between corresponding signals from thewavefront sensor 7. For many types of wavefront sensors 7, a referencecalibration or zero-point calibration is additionally required. Such areference calibration is provided through the various embodiments of thepresent invention.

When performing a reference calibration according to various embodimentsof the present invention, a reference light-source (not shown in FIG. 1a) is inserted at a suitable position on the common path 2 between theobject 5 and the controllable wavefront-modifying device 9. Anadvantageous choice of position may be the same exemplary position “X”designated for the point source(s) in the above-mentioned relativecalibration.

It should be noted that the adaptive optics system 1 described abovewith reference to FIG. 1a is a simplified system, which only includesthe key components of an adaptive optics system. In reality, as is wellknown to those skilled in the art, an adaptive optics system includes,depending on the field of application, various additional optics forshaping the various light-beams and for providing for adjustability andtuning of the adaptive optics system. A more detailed description of anadaptive optics system for which the reference calibration according tovarious embodiments of the present invention would be suitable isprovided by U.S. Pat. No. 7,639,369, which is hereby incorporated byreference in its entirety.

As was touched upon above, the adaptive optics system 1 in FIG. 1a iscontrollable to operate at least in a calibration mode and in aregulation mode. In each of these states, the various parts of theadaptive optics system 1 are controlled by the control system 10, whichwill be described in more detail below with reference to the schematicblock diagram in FIG. 1 b.

With reference to FIG. 1b , the control system 10 comprises an output 20for providing control signals S_(WMD) to the wavefront modifying device9, a first input 21 for receiving signals S_(WS) from the wavefrontsensor 7, and a second input 22 for receiving signals S_(DD) from thedetecting device 8. As is schematically indicated in FIG. 1b , thecontrol system 10 further comprises a wavefront modifying devicecontroller 23 for controlling the wavefront modifying device 9,calibration circuitry 24 for determining calibration parameters for theadaptive optics system 1, and a memory 25 for storing the calibrationparameters.

In the regulation mode, the wavefront modifying device controller 23controls the wavefront modifying device 9 based on signals from thewavefront sensor 7, and the calibration parameters stored in the memory25. The purpose of the regulation is to control the wavefront modifyingdevice 9 to keep the wavefront associated with the guide-star(s)constant at the wavefront sensor 7 and thereby continuously compensatefor variations in the optical properties between the object 5 and thewavefront sensor 7.

The calibration parameters stored in the memory 25 are crucial to theability of the adaptive optics system 1 to accurately perform theabove-mentioned regulation. The calibration parameters are thereforeadvantageously determined based on both a relative calibration asbriefly described above and a reference calibration. In the following, areference calibration method according to an exemplary embodiment of thepresent invention will be described with reference to the flow chart inFIG. 2, as well as with continued reference to FIGS. 1a -b.

In the first step 100, a reference light-source is arranged on thecommon path 2, for example at the position denoted “X” in FIG. 1 a.

For each of a number of orthogonal wavefront modes, the wavefrontmodifying device 9 is then controlled to vary the magnitude of theorthogonal wavefront mode over a number of magnitude settings. In FIG.2, this is illustrated as a double loop where a number of steps areperformed for each magnitude setting j for a given orthogonal wavefrontmode n, and a number of steps are performed for each orthogonalwavefront mode n once the steps of all magnitude settings j have beencarried out.

In FIG. 2, the steps performed for each magnitude setting j are denoted101-105. In step 101, orthogonal wavefront mode n of the wavefrontmodifying device 9 is controlled to magnitude j by the wavefrontmodifying device controller 23. Subsequently, in step 102, a reading jof the detecting device 8 corresponding to magnitude setting j isacquired through the second input 22 of the control system 10.Thereafter, in step 103, a quality metric value is determined by thecalibration circuitry 24. The quality metric value is indicative of theinformation content of reading j and may for example indicate adeviation between a known properties of the reference light beam and theproperties of the reference light beam detected by the detecting device8. When steps 101-103 have been carried out for magnitude setting j, itis checked in step 104 if all magnitude settings have been steppedthrough, that is if j=j_(max). If this is not the case, the magnitudesetting counter is incremented by 1 in step 105, and steps 101-104 arerepeated. If j=j_(max), the method proceeds to step 106, in which thecalibration circuitry 24 determines a reference parameter set for thewavefront modifying device 9 corresponding to an optimum quality metricvalue for the current orthogonal wavefront mode n based on the qualitymetric values determined for the different magnitude settings j. Thisdetermination of reference parameter set may advantageously be performedthrough a curve fit of the pairs of magnitude settings and correspondingquality metric values to a predefined function.

After having determined the reference parameter set for orthogonalwavefront mode n, it is checked in step 107 if all orthogonal wavefrontmodes have been stepped through, that is if n=n_(max). If this is notthe case, the orthogonal wavefront mode counter is incremented by 1 instep 108, and steps 101-107 are repeated. Before returning to step 101,the orthogonal wavefront modes that have already been cycled through maybe set according to their determined reference parameter sets. It hasbeen empirically established that this generally results in a fastercalibration than if the other orthogonal wavefront modes (other thanorthogonal wavefront mode n) are controlled to a predefined settingduring the magnitude variation of orthogonal wavefront mode n.

If n=n_(max), the method proceeds to step 108 and provides a referencecalibration setting for the adaptive optics system 1 based on thereference parameter sets for the orthogonal wavefront modes.

EXAMPLE Theoretical Discussion and Experimental Setup

Theoretical Discussion

Quality metrics for general objects have been considered, but given thefact that the interaction matrix of most adaptive optics systems iscalibrated with a point source, the discussion here will be limited tothat. Image plane quality metrics can then be encircled energy radius,I^(n) (X) where I(x) is the focal plane intensity etc. A commonly usedmetric that describes the performance of an adaptive optics system isthe Strehl ratio:S=I(0,0)/I _(★)(0,0)=∫Ĩ(f)df/∫Ĩ _(★() f)df≈exp(−σ_(Φ) ²),  (1)

where I(0,0) is the on-axis image intensity, I_(★)(0,0) is the on-axisaberration-free image intensity in the focal plane and denotes theFourier transform. The second equality is a consequence of the definiteintegral theorem, and following that, the Marèchal approximation isgiven, valid for phase deviations conforming to Gaussian statistics. TheMarèchal approximation is seen to describe a Gaussian function of theRMS pupil phase error σ_(Φ), but is also commonly given in a quadraticform S≈1−σ_(Φ) ². Both approximations are valid for σ_(Φ)<<1. Looking atsimulated Strehl values for the Zernike modes from 2nd to 5th radialorder, it is seen that the Strehl value will approximate a Gaussianfunction exp (−σ_(Φ) ²) over a larger aberration interval than thequadratic decay 1−σ_(Φ) ². If the actual tip-tilt contribution isneglected, which does not affect the image quality, the peak intensityis found at x_(max)=arg max_(x)I(x) and according to the shift theoremit is found thatS _(⊥) =I(x _(max))/I _(★)(0,0)=∫Ĩ(f)exp(i2πfx _(max))df/∫Ĩ_(★)(f)df≈exp(−τ_(Φ) _(⊥) ²).  (2)

It is obvious from this expression that minimizing the phase error (thepurpose of an adaptive optics system) is identical to maximizing thenumerators. In the discrete 21st century, an image sampled at or nearthe Nyquist-limit will suffer from severe discretization implying thatthe spatial domain has been found less suitable for the task ofestimating the Strehl value. In case it is used, it is common to changethe sampling interval by zero-padding in the Fourier domain followed byinverse transformation. Since all information is contained within theFourier domain, the quality metric used here is based on the Fouriertransformed image. For a discrete image/from the CCD/CMOS detector,where the pixel coordinates are given by the positive integers r and s,the sub-pixel shift in the image domain (x_(max), y_(max)) is estimatedwith a quadratic interpolation around the maximum pixel intensity valueat I_(r) _(max) _(s) _(max) giving:

$\begin{matrix}{{y_{\max} = {\left( {r_{\max} - {m/2} - 1} \right) + \frac{I_{{({r_{\max} - 1})}s_{\max}} - I_{{({r_{\max} + 1})}s_{\max}}}{2\left\lbrack {I_{{({r_{\max} - 1})}s_{\max}} + I_{{({r_{\max} + 1})}s_{\max}} - {2\; I_{r_{\max}s_{\max}}}} \right\rbrack}}},} & (3)\end{matrix}$

and analogous for x_(max). The continuous pixel coordinates x and y havean origin in the center if the discrete image, hence the subtraction ofm/2+1 as the image format is m×m. The quality metric value according tothis exemplary embodiment of the invention is then given by the discreteversion of the Fourier domain numerator in Eq. (2)Q=Σ _(r=1) ^(m)Σ_(s=1) ^(m) Ĩ _(rs)exp(i2π[(r−m/2−1)y _(max)+(s−m/2−1)x_(max) ]/m).  (4)

It is seen that maximizing this quality metric value will minimize thewavefront error and maximize the Strehl ratio. Ĩ_(rs) is the discreteFourier transform (e.g. using FFT) of the point source image Ĩ_(rs).Since the image intensity is a real function, its Fourier transform willbe Hermitian, i.e., Ĩ(−f)=Ĩ*(f), and the imaginary part will cancel outto give a real quality metric value. Hence the summation can be limitedto the real part in half of the Fourier domain, to speed up thecalculations of the quality metric value.

The phase imposed in a pupil plane by an exemplary waveform modifyingdevice in the form of a deformable mirror with k actuators can bedescribed byΦ(ξ)=Σ_(k) c _(k)Φ_(k) ^(I)(ξ),  (5)

where Φ_(k) ^(I)(ξ) is the point response function, or influencefunction, of a unit actuator command c_(k)=1. The phase is measured bythe wavefront sensor producing the measurement vector s. Duringreference calibration of an adaptive optics system, the interactionmatrix s=Gc is obtained by measuring the impulse response of eachactuator and collecting these wavefront sensor measurements as columnsin G. During closed loop (in the regulation mode) the (truncated)pseudoinverse is used to update the shape of the deformable mirrorc=G⁺s, and common in the control of adaptive optics systems is to obtainthe singular value decomposition G=VΛU^(T). The columns of V and U,v_(m) and u_(n), are the left and right singular modes definingorthonormal vectors in sensor measurement space and actuator commandspace respectively. These are also ordered according to sensitivity,starting with the most sensitive modes. Hence each singular mode is anorthogonal phase distribution according to Eq. (5), i.e.Φ_(n)(ξ)=Σ_(k) U _(kn)Φ_(k) ^(I)(ξ)  (6)and changing the magnitude of this phase mode to α_(n)Φ_(n)(ξ)corresponds to applying the actuator commands α_(n)u_(n). It iscertainly common to use also other orthogonal expansions, e.g. Zernikepolynomials, to describe the phase, but the SVD method offers to anatural decomposition of the adaptive optics system's inputs and outputswithout any further approximations, simultaneously grading thesensitivity of the singular modes. The exemplary method presented hereexploits scanning of the orthogonal singular modes Φ_(n)(ξ). Accordingto Eqs. (1-4) the quality metric value Q will follow a Gaussian functionfor small aberrations. Hence, for each scanned singular mode (changingα_(n) over j points) a least squares fit gives:

$\begin{matrix}{\begin{bmatrix}{\hat{a}}_{n} \\{\hat{b}}_{n} \\{\hat{k}}_{n}\end{bmatrix} = {\arg\;{\min_{a_{n},b_{n},k_{n}}{\sum\limits_{j = 1}^{j_{\max}}\;{{Q_{j} - {k_{n}{\exp\left( {- \frac{\left( {\alpha_{n,j} - \alpha_{n}} \right)^{2}}{b_{n}^{2}}} \right)}}}}^{2}}}}} & (7)\end{matrix}$

where the last term in the squared norm defines a Gaussian function,given by the parameters a_(n), b_(n) and k_(n). The peak of theestimated function is found at â_(n), and hence for a specific singularmode, the Strehl is maximized and the wavefront error is minimized forâ_(n)Φ_(n)(ξ). As all singular modes have been optimized, the mirrorshape that optimizes the performance of the adaptive optics system willbe c_(★)=Σ_(n)â_(n)u_(n). An advantage of this exemplary embodiment ofthe method according to the present invention is that all parametersthat are needed to achieve the optimization are already available inmost adaptive optics systems, and it can be executed immediately afterthe interaction matrix has been calibrated without any alteration of thesetup, but simply with the provision of a reference light-source. Nofurther assumptions need to be made, nor is any additional equipment oralteration of the optical system needed.

There are of course limitations on the possible level of correction forthe method. Due to the orthogonality of the singular modes, the methodwill not converge to a local maximum. However, for the case of severeinitial aberrations (no core in the point spread function) severaliterations of the method may be required. For the practicalimplementation of the correction procedure, when a new calibration isneeded we have found it useful to start the new calibration from thepreceding calibration of the wavefront modifying device, i.e. from theold command vector c_(★), since the quasi-static aberrations in theimaging path are likely similar. Likewise, the first 10 modes mayadvantageously be scanned twice, since loss of alignment and thermallyinduced errors will plausibly introduce low-order aberrations such asastigmatism and coma, and these are commonly present among thewell-sensed modes of the adaptive optics system.

EXPERIMENTAL SETUP

The exemplary method presented above has been implemented in anophthalmic adaptive optics instrument such as that described in U.S.Pat. No. 7,639,369. A single mode optical fiber has been used as a pointsource (A=635 nm) on the common path, and the point spread function hasbeen optimized according to the method given above. The sampling of theCCD detector corresponds to Nyquist sampling. The scan interval of eachmode was adjusted individually, with an increasing interval of α_(n) foreach mode, roughly corresponding to τ_(Φ)≈[−0.15, 0.15] waves. Likewise,the number of modes n_(max) to optimize was limited since it was obviousthat that ill-sensed modes did not follow the Marèchal approximation,and the threshold was set according to this criterion. The first 10modes were optimized twice, since most of the energy is likely containedwithin these modes. The number of scan points was j_(max)=10.

The peak intensity position of the resulting point spread function hasbeen estimated according to Eq. (3), applying this phase shift to theFourier transformed image according to Eq. (2), which then generates thecentred point spread function through an inverse Fourier transform. Theintensity of the central pixel was then compared to the ideal pointspread function, where the energy in both point spread functions wereadjusted to the same level.

The invention claimed is:
 1. An adaptive optics system for providingaberration compensated detection of light from an object, the adaptiveoptics system comprising: a detecting device for detecting light fromsaid object; a wavefront sensor configured to provide signals indicativeof a spatial phase distribution of light incident on the wavefrontsensor; at least one controllable wavefront modifying device arrangedsuch that light from said object passes via said wavefront modifyingdevice to said detecting device and to said wavefront sensor; a controlsystem connected to the wavefront sensor and to the wavefront modifyingdevice, said control system being operable in a calibration mode and ina regulation mode, wherein said control system comprises: an output forproviding control signals to the wavefront modifying device; a firstinput for receiving signals from the wavefront sensor; a second inputfor receiving readings the detecting device; a wavefront modifyingdevice controller for controlling the wavefront modifying device;calibration circuitry for determining calibration parameters for theadaptive optics system; and a memory for storing said calibrationparameters, wherein: when said control system operates in saidcalibration mode: said wavefront modifying device controller, for eachof a plurality of orthogonal wavefront modes of the wavefront modifyingdevice, controls the wavefront modifying device to vary a magnitude ofthe orthogonal wavefront mode over a predetermined number of magnitudesettings; and said calibration circuitry, for each of the plurality oforthogonal wavefront modes, determines a quality metric value indicativeof an information content of each reading in a series of readingsreceived from the detecting device, each reading corresponding to one ofsaid magnitude settings, resulting in a series of quality metric values;determines a reference parameter set for the wavefront modifying devicecorresponding to an optimum quality metric value based on the series ofquality metric values for each of said plurality of orthogonal wavefrontmodes; and when said control system operates in said regulation mode:said wavefront modifying device controller regulates the wavefrontmodifying device based on signals from the wavefront sensor and saidreference parameter set.
 2. The adaptive optics system according toclaim 1, wherein, when the control system is in said calibration mode,said calibration circuitry further determines an interaction matrixdefining a relation between different wavefront modifying states of thecontrollable wavefront modifying device and corresponding signals fromthe wavefront sensor.
 3. The adaptive optics system according to claim1, wherein said wavefront modes are based on said interaction matrix. 4.The adaptive optics system according to claim 1, wherein, when thecontrol system is in said calibration mode, said calibration circuitryfurther, for each of said plurality of wavefront modes, controls thewavefront modifying device using said reference parameter set.
 5. Theadaptive optics system according to claim 1, wherein, when the controlsystem is in said calibration mode, said calibration circuitrydetermines said optimum quality metric value by fitting said series ofquality metric values to a predetermined function having a maximum orminimum corresponding to a minimum aberration of the wavefront mode.